I really like Forgotten Realms because it has been so fleshed out, but still huge and allows you to do your own thing without much effort.
Back in them olden days when Jim Butler's company scanned and sold all the D&D books for $2.99/book I bought pretty much everything and created a FR pdf catalog for quickly searching all the FR pdfs. That was Extremely useful for running a FR adventure and campaign. Add to that the FR Interactive Atlas and I could do pretty much anything with FR. I think I even used it to run the fan made
Northern Journey campaign with the bits and pieces Eric Noah collected on this site for 3E, as a 3E campaign.
I really liked the information dense 3e FR core book. And the maps! Or the even bigger maps from Dragon Magazine! Although I did not like everything they did in/for 3E or in the FR novels.
I really dislike the 100 year leap they did for 4E and 5E progressing from there is not something I like either. Just as I don't like all the 'new' default species options in the PHB like Dragonborn, Half-Orc, Tiefling, etc. Don't get me wrong, I loved the 2E Complete Book of Humanoids! But I just don't want those as default PC options, just as I don't like Drow being a default PC option (although Drizzt spoiled it for everyone!)...
Now, with looking at 5E, Baldur's Gate 3, etc. I don't see a FR happening from WotC. Now, I understand the '+' of this thread, so I interpret that as a fan made reboot of FR.
From that perspective I would personally fit the reboot to the group you're playing with and having a huge digital library for that makes things easy. You just add notes to the source material or compile a whole new player guide. I'm actually curious if you could feed something like ChatGPT FR lore, set restrictions and just let it generate a whole new guide for you...
From DMing 3(.5)E I would start with a restrictions list for whatever rule set you're playing with, which books the players use, what is restricted in each of those books. With me (our group) things might be discussed, but they would need to have a very good reason for that and everyone would need to be OK with that. Define a starting year and which big events that didn't happen. Chances are that some know something of FR and their assumptions need to be addressed. What that is exactly, totally depends on who you're playing with imho.
The Wall of the Faithless goes. This is not open to negotiation.
Depending on who you run with, this could totally stay. I'm Agnostic and do not find this offensive at all. It was after all made by an evil god. I could even introduce something like Faith of the Void, which does exactly what people believe it does or it might not (might be a deceiver at play). The players don't know, nor do their characters, especially not at low level. If they are plane hopping at high levels, the might be confronted by Demons wanting to raid the wall for souls. Good, Evil or Neutral organizations (possibly backed by certain deities) that want to abolish the wall. Again, depending who you're playing with this can be the main plot device to just being there in the background. Or if I'm playing with people who are as adamant about it as you are, it might just not exist at all.